{"paper":{"title":"Existence of positive solutions to a nonlinear elliptic system with nonlinearity involving gradient term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ahmed Attar, Boumediene Abdellaoui, El-Haj Laamri","submitted_at":"2017-09-10T08:47:03Z","abstract_excerpt":"In this work we analyze the existence of solutions to the nonlinear elliptic system: \\begin{equation*} \\left\\{ \\begin{array}{rcll} -\\Delta u & = & v^q+\\a g & \\text{in }\\Omega , \\\\ -\\Delta v& = &|\\nabla u|^{p}+\\l f &\\text{in }\\Omega , \\\\ u=v&=& 0 & \\text{on }\\partial \\Omega ,\\\\ u,v& \\geq & 0 & \\text{in }\\Omega, \\end{array}% \\right. \\end{equation*} where $\\Omega$ is a bounded domain of $\\ren$ and $p\\ge 1$, $q>0$ with $pq>1$. $f,g$ are nonnegative measurable functions with additional hypotheses and $\\a, \\l\\ge 0$.\n  As a consequence we show that the fourth order problem \\begin{equation*} \\left\\{ \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03070","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}